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Simplifying x2 + 4x + -45 = 9 Reorder the terms: -45 + 4x + x2 = 9 Solving -45 + 4x + x2 = 9 Solving for variable 'x'. Reorder the terms: -45 + -9 + 4x + x2 = 9 + -9 Combine like terms: -45 + -9 = -54 -54 + 4x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -54 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 4x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 4x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 4x + x2 = 0 + 54 4x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 4x + x2 = 54 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 54 + 4 Reorder the terms: 4 + 4x + x2 = 54 + 4 Combine like terms: 54 + 4 = 58 4 + 4x + x2 = 58 Factor a perfect square on the left side: (x + 2)(x + 2) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 2) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 2 = 7.615773106 Simplifying x + 2 = 7.615773106 Reorder the terms: 2 + x = 7.615773106 Solving 2 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.615773106 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.615773106 + -2 x = 7.615773106 + -2 Combine like terms: 7.615773106 + -2 = 5.615773106 x = 5.615773106 Simplifying x = 5.615773106Subproblem 2
x + 2 = -7.615773106 Simplifying x + 2 = -7.615773106 Reorder the terms: 2 + x = -7.615773106 Solving 2 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.615773106 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.615773106 + -2 x = -7.615773106 + -2 Combine like terms: -7.615773106 + -2 = -9.615773106 x = -9.615773106 Simplifying x = -9.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.615773106, -9.615773106}
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